Document Zbl 0406.57003

Deformation of maps to branched coverings in dimension three. (English) Zbl 0406.57003

Math. Ann. 245, 273-279 (1979).

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MSC:

57M12	Low-dimensional topology of special (e.g., branched) coverings
57N10	Topology of general \(3\)-manifolds (MSC2010)
57N70	Cobordism and concordance in topological manifolds
57Q55	Approximations in PL-topology

Keywords:

Closed Orientable 3-Manifolds; Branched Covering; Degree; Epimorphisms of Fundamental Groups; Homotopic to a Piecewise Linear Open Map

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Full Text: DOI EuDML

References:

[1]	Berstein, I., Edmonds, A.L.: On the construction of branched coverings of low-dimensional manifolds. Trans. Am. Math. Soc.247, 87–124 (1979) · Zbl 0359.55001 · doi:10.1090/S0002-9947-1979-0517687-9
[2]	Berstein, I., Edmonds, A.L.: The degree and branch set of a branched covering. Invent. Math.45, 213–220 (1978) · doi:10.1007/BF01403169
[3]	Berstein, I., Edmonds, A.L.: Classification of surface maps modulo self-equivalences. In preparation, abstract in AMS Notices (Feb. 1978)
[4]	Cappell, S.E.: A splitting theorem for manifolds. Invent. Math.33, 69–170 (1976) · Zbl 0348.57017 · doi:10.1007/BF01402340
[5]	Edmonds, A.L.: Deformation of maps to branched coverings in dimension two. Ann. Math.110, 113–125 (1979) · Zbl 0424.57002 · doi:10.2307/1971246
[6]	Epstein, D.B.A.: The degree of a map. Proc. London Math. Soc. (3)16, 369–383 (1966) · Zbl 0148.43103 · doi:10.1112/plms/s3-16.1.369
[7]	Fox, R.H.: A note on branched cyclic coverings of spheres. Rev. Mat. Hisp.-Am.32, 158–166 (1972) · Zbl 0246.55001
[8]	Hempel, J.: 3-Manifolds. Ann. Math. Study 86. Princeton: Princeton University Press 1976
[9]	Hilden, H.M.: Three-fold branched coverings ofS 3. Am. J. Math.98, 989–997 (1976) · Zbl 0342.57002 · doi:10.2307/2374037
[10]	Hirsch, U.: Über offene Abbildungen auf die 3-Sphere. Math. Z.140, 203–230 (1974) · doi:10.1007/BF01214163
[11]	Hirsch, U.: On regular homotopy of branched coverings of the sphere. Manuscripta Math.21, 293–306 (1977) · Zbl 0423.57001 · doi:10.1007/BF01167881
[12]	Hirsch, U., Neumann, W.: On cyclic branched coverings of spheres. Math. Ann.215, 289–291 (1975) · doi:10.1007/BF01343895
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[14]	Laudenbach, F.: Topologie de la dimension trois: homotopie et isotropie. Asterisque12, Paris, 1974 · Zbl 0293.57004
[15]	Montesions, J.M.: Three-manifolds as 3-fold branched covers ofS 3. Q. J. Math. Oxford (2)27, 85–94 (1976) · Zbl 0326.57002 · doi:10.1093/qmath/27.1.85
[16]	Montesions, J.M.: 3-variétés qui ne sont pas des revêtesments cycliques ramifiés surS 3. Proc. Am. Math. Soc.47, 495–500 (1975). Corrigendum: Proc. Am. Math. Soc.53, 541 (1975)
[17]	Rourke, C.P., Sanderson, B.J.: Block bundles II, transversality. Ann. Math.87, 255–277 (1968) · Zbl 0215.52301
[18]	Stallings, J.: On fibering certain 3-manifolds. In: Topology of 3-manifolds (ed. M.K. Fort). Prentice Hall, 95–100 (1962) · Zbl 1246.57049
[19]	Walsh, J.J.: Monotone and open mappings on manifolds. I. Trans. Am. Math. Soc.209, 419–432 (1975) · Zbl 0304.57010 · doi:10.1090/S0002-9947-1975-0375326-0

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